Robust mixture regression modeling based on the generalized M (GM)-estimation method

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Dogru F. Z., ARSLAN O.

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, vol.50, pp.2643-2665, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50
  • Publication Date: 2021
  • Doi Number: 10.1080/03610918.2019.1610442
  • Journal Name: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Computer & Applied Sciences, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2643-2665
  • Keywords: EM algorithm, GM-estimation method, M-estimation method, mixture regression models, robust regression, MAXIMUM-LIKELIHOOD, DISTRIBUTIONS
  • Ankara University Affiliated: Yes

Abstract

A robust mixture regression based on the M regression estimation method has already been proposed in literature. However, since the M-estimators are only robust against the outliers in response variables, the resulting mixture regression methods will not be robust against the outliers in explanatory variables (leverage points). In this paper, we propose a robust mixture regression procedure to handle the outliers and the leverage points, simultaneously. Our proposed mixture regression procedure is based on the GM regression estimation method. We give an EM-type algorithm to compute estimates for the parameters of interest. We provide a simulation study and a real data example to assess the robustness performance of the proposed method against the outliers and the leverage points.